At low frequencies is also
large (
-> 2 when 0-frequency
isotropic
conductivity dominates the dielectric tensor), so that the temperature
changes only slowly with radius at the outskirts of the galaxy (~ 3 -
30 kpc) where the molecular gas distribution of galaxies rapidly
becomes very patchy. The characteristic temperature at the outskirts
of a typical galaxy would be ~ 30 - 50 K (see
figure 1).
![]() |
Figure 1. Temperature of directly illuminated 0.1 µm graphite grains as a function of distance from a central UV source of luminosity LUV = 1046 erg s-1. Planck-averaged absorption efficiencies used are from Draine & Lee 1984. For sources of other luminosities and grains of other sizes, the temperature in the flatter portions of the curve (T > 300 K, T < 60 K) scales roughly as (LUV / a)1/6, and in the steeper portion (60 K < T < 300 K) as (LUV / a)1/4. For a galaxy disk with a smooth logarithmic warp, dust at the given temperatures contributes predominately to the flux at wavelengths marked on the right. |
A dust layer wil absorb UV flux incident at an angle to the normal
of the layer if its column density
> 10-2 cos
g cm-2. With a
Galactic gas-to-dust ratio spread over a disk of radius
rkpc this
column corresponds to a mass of gas MH
2 x 108 cos
r2kpc M
. The gas
masses in nearby AGN are inferred from observations of CO (which of
course depletion relates more directly to the dust than to
MH!) to be
of order 108-1010 M
(Sanders, Scoville,
& Soifer 1988a),
and even in
a young galaxy such as might surround a high redshift quasar it is
unlikely that there would be more than ~ 1011
M
of processed
gas. Consequently the disk will become optically thin beyond a few kpc
(it could become thin at a smaller radius if most of the dust is
clumped into clouds with
>>
10-2 cos
g
cm-2, and such clouds at
larger radii could preserve dust in neutral cores, but their covering
factor would necessarily be very small).
Since the covering factor of dusty material at 20 K (~ 100 kpc) is
expected to be very small, the spectrum of dust reradiation will be
characterized by a rather well-defined minimum temperature, and should
roll over sharply at wavelengths
200
µm with F
2+
at longer
wavelengths (as for similar reasons it is observed to do in starburst
galaxies and Galactic H II regions - cf.
Telesco & Harper
1980).
The precise form of the spectrum at 60 µm <
< 200 µm will
vary depending
on the covering factor at large radius, which could be enhanced by the
presence of companion galaxies (whose starlight maintains a minimum
dust temperature ~ 20 K!), tidal tails, and the like.
As we discuss in section 5, at frequencies
< 1011 Hz, free-free
emission from photoionized gas at the illuminated face of the disk
will dominate the spectrum. Figure 2 shows the
spectrum of continuum
reradiation from gas and dust in an exponential disk with a
logarithmic warp (d(covering factor) / d ln r =
const). To illustrate how
material at large radii can affect the far infrared and submillimeter
spectrum, we show the effect of adding reradiation from a 2 x 20 kpc
slab of dust extending from 10 to 30 kpc (which could represent a
companion galaxy or a tidal tail).